Depending on the length of the run of pipe, you may reach a point where regardless of what you do, the size of the pipe will limit the amount of air that can be moved. That amount of air may be less than what is required to adequately ventilate the room safely. I doubt you can get much more than a two inch piece of pipe from the basement up to through the roof, so some math will be in order.

You need to figure out how much volume of air you need to replace, and at what pressure will be required to get that much air through the size of pipe you are using. Don't forget to calculate in the pressure drops due to elbows, bends, etc. I know for bathrooms, you need to exchange the air eight times per hour, or about 1CFM per square foot or area. I am not sure of the number of times you would need to exchange the air while painting.

To me, the bottom line is it will help, but you will likely find your suggested method inadequate.